Existence of Positive Solutions for a Nonlinear Third-order Integral Boundary Value Problem

TL;DR

This paper proves the existence of positive solutions for a nonlinear third-order boundary value problem with integral conditions using Krasnoselskii's fixed point theorem, expanding the understanding of such differential equations.

Contribution

It introduces a new approach employing Krasnoselskii's fixed point theorem to establish positive solutions for complex third-order boundary value problems with integral conditions.

Findings

Existence of at least one positive solution is proven.

The method applies Krasnoselskii's fixed point theorem on cones.

Results extend previous work on boundary value problems with integral conditions.

Abstract

In this paper, we study the existence of at least one positive solution for a nonlinear third-order two-point boundary value problem with integral condition. By employing the Krasnoselskii's fixed point theorem on cones, the existence results of the problem are established.